This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A223936 #62 Nov 02 2024 04:06:48
%S A223936 2,97,3877,4943,50741,1487159,3356117,131047091863,449627893189,
%T A223936 906460844407,61168531626487,141835115384731,749668095960389,
%U A223936 1259394274876189,3849791511371129,6669425423437787,11674340378841221,75041264698436783
%N A223936 Numbers prime(m), such that (Sum_{i=1..m} prime(i)^3) / m is an integer.
%H A223936 OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e A223936 a(2) = 97, because 97 is the 25th prime and the sum of the first 25 primes^3 = 4696450 when divided by 25 equals 187858 which is an integer.
%t A223936 k = 1; p = 2; s = 0; lst = {}; While[p < 1000000000, s = s + p^3; If[ Mod[s, k++] == 0, AppendTo[lst, p]]; p = NextPrime@ p]; lst
%Y A223936 Cf. A085450 (smallest m > 1 that divides Sum_{k=1..m} prime(k)^n).
%Y A223936 Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y A223936 Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K A223936 nonn,more
%O A223936 1,1
%A A223936 _Robert Price_, Mar 29 2013
%E A223936 a(11) from _Paul W. Dyson_, Jan 05 2021
%E A223936 a(12) from _Bruce Garner_, Mar 01 2021
%E A223936 a(13) from _Bruce Garner_, Apr 06 2021
%E A223936 a(14) from _Bruce Garner_, May 13 2021
%E A223936 a(15) from _Bruce Garner_, Jan 08 2022
%E A223936 a(16) from _Paul W. Dyson_, Jan 17 2022
%E A223936 a(17) from _Bruce Garner_, Jul 31 2022
%E A223936 a(18) from _Paul W. Dyson_, Feb 18 2024